Differential Evolution in Wireless Communications:
A Review
https://doi.org/10.3991/ijoe.v15i11.10651
Hilary I. Okagbue
(*) Covenant University, Ota, NigeriaMuminu O. Adamu
University of Lagos, Lagos, Nigeria
Timothy A. Anake
Covenant University, Ota, Nigeria
Abstract—Differential Evolution (DE) is an evolutionary computational method inspired by the biological processes of evolution and mutation. DE has been applied in numerous scientific fields. The paper presents a literature re-view of DE and its application in wireless communication. The detailed history, characteristics, strengths, variants and weaknesses of DE were presented. Seven broad areas were identified as different domains of application of DE in wire-less communications. It was observed that coverage area maximisation and en-ergy consumption minimisation are the two major areas where DE is applied. Others areas are quality of service, updating mechanism where candidate posi-tions learn from a large diversified search region, security and related field ap-plications. Problems in wireless communications are often modelled as multi-objective optimisation which can easily be tackled by the use of DE or hybrid of DE with other algorithms. Different research areas can be explored and DE will continue to be utilized in this context.
Keywords—Differential evolution, multiobjective optimisation, evolutionary computation, energy utilisation, localisation, coverage, wireless networks.
1
Evolutionary Computation
Optimisation is central to many natural processes as the method of evolution, memes
and adaptation implies that organisms attempt to adjust over time to fit in optimally to
their environment despite the constraints of space, search for food, shelter, and search
for mates and so on. The study of these natural processes gave birth to the notion of
computational intelligence of which evolutionary computation is a subfield [4].
EC is a family of iterative algorithms inspired mostly by biological evolution and
are employed mostly in global optimisation [5]. In addition, is a branch of applied
mathematics that deals with the global optimisation of a given function or set of
func-tions based on some predefined criteria. Global optimisation focuses on finding the
maximum or minimum of all input values while local optimisation deals with finding
local minima or maxima.
In EC, an initial set of candidate solutions is generated and iteratively updated to
minimise or maximise the given function [6]. Each new solution (generation) is
pro-duced by stochastically removing weaker or less desired solutions – survival of the
fittest and iteratively introducing random changes until a termination criterion that
guarantee a feasible solution is obtained [7]. EC techniques can produce highly
opti-mized solutions given a wide range of constraints and complex objective function [8].
This makes EC a suitable tool for solving multi-dimensional problems and advanced
optimisation [9].
The choice of EC is mainly based on the nature of the problem to be solved and the
corresponding data structures. EC techniques perform well in solving higher
proce-dure problems that are designed to find, select or search or determine a heuristic
(par-tial search algorithm) that obtain a near optimal solution [10]. EC works with
incom-plete or partial, or imperfect information and limited completion capacity [11].
How-ever, EC does not guarantee that an optimal (exact) solution will be obtained [12].
Differential evolution (DE) is one of the most widely used EC technique [13-15].
The biological processes of evolution, mutation and adaptation inspired the
develop-ment of DE.
The aim of this review is to critically analyse the different areas where DE has
been applied in wireless communications.
2
Differential Evolution
The basic procedure of Differential evolution (DE) is given. A population of
can-didate solutions (called vectors) is moved around in the search space by using the
mathematical formulae defined for the objective (fitness) function to combine the
positions of existing vectors from the population. If the new position of the vector is
an improvement, then it is accepted and promoted to form part of the population.
Otherwise, the new position is simply discarded and sometimes archived. The process
is repeated t times until a satisfactory solution is discovered. Note that the algorithm
does not guarantee that an optimal (exact) solution will be found.
Let
, be the fitness function, which must be minimised, based on
some equality, inequality or bounded constraints. The function maps a candidate
solu-tion in the form of vector in a given dimensional space to a real number as output,
:
nwhich indicates, the fitness of the given candidate solution. The aim is to find m for
which
for all p in the search space of the given dimension, which
means that the solution m is the only global minimum available.
The detailed development, component, variants, application areas and application
of DE in curve fitting are presented here.
2.1
Historical development
The DE algorithm was created to be a very vital force in evolutionary computing.
The first articles on DE was basically introductory [16] and it took a year later to
actually demonstrate the computational efficiency of the method in an IEEE
interna-tional contest built in conference [17], where it tops other EA in solving real-valued
functions. Researchers were interested in the method and some papers were published
to further elucidate the theory, processes and mathematics behind the method, which
give birth to a clearer DE algorithm. The papers are [16] and [18-19]. Since then, DE
has proven to be a force to be reckoned with, in EC. Summary of the method can be
found in [20] and [21], and their references therein.
In the application of DE, the individual candidate (trial) solutions are called
param-eter vectors or genomes. DE utilizes difference of the paramparam-eter vectors to assess and
explore the objective function landscape, which is a deviation from the other EA. The
reliance of DE on difference vectors can be traced to earlier algorithms which uses
difference vectors in their computation. The algorithms are Nelder-Mead algorithm
[22] and the controlled random search algorithm [23].
According to [24[, the reasons why DE is used by researchers as a reliable
optimi-sation tools are listed.
1.
DE is simpler and easier to implement when compared with other evolutionary
al-gorithms. The code is easy to code with different programming languages and can
easily be understood by novices.
2.
The performance is better than most EC in terms of convergence, computational
speed, accuracy and robustness [25]. This makes it a suitable candidate for
han-dling unimodal, multimodal, homogenous, homogenous, separable and
non-separable systems [26].
3.
The number of control parameters (Cr, F, and NP) in DE is very few. This has
helped to reduce the computational burden associated with the method [27].
4.
The low space complexity of DE has been helpful in the use of DE for solving
large scale, nonlinear and multi-dimensional optimisation problems.
2.2
Control parameters of the differential evolution
There are three main control parameters of the DE algorithm: the mutation scale
factor F, the crossover constant Cr and the population size NP [24]. A good choice of
the control parameters is necessary for the efficient execution of the DE [28]. It is
recommended that for the one-dimensional case, the least population size is 4,
muta-tion factor is set as 0.5 and the crossover constant should be adjusted between 0 and 1
( )
( )
and this has to be problem specific since some objective functions tend to be sensitive
to the choice of the control parameters [29]. Wrong choice of these parameters will
ultimately frustrate the algorithm, leading to slow convergence speed and inaccurate
results [30].
2.3
Different variants of differential evolution
Since the introduction of DE, researchers have continued to propose different
vari-ants of the algorithm without necessarily altering its foundation. The nonlinear and
complex nature of some problems have led researchers to push back the boundaries of
DE. The different variants of DE are listed.
Differential evolution using trigonometric mutation:
This was proposed by [31],
aimed at speeding up the performance of DE by splitting the target vectors [32].
Differential evolution using arithmetic recombination:
This comes as a
depar-ture from the traditional binomial crossover used in DE. Here, recombination can be
either continuous or arithmetic. The trial vector is now expressed as a linear
combina-tion of the components from the donor and target vectors [33]. Furthermore, the
coef-ficients of the combination can be a random variable or constant [34].
DE/rand/1/either-or algorithm:
This variant of the DE algorithm was designed in
such a way that the here the trial vectors that are pure mutants and those that are pure
recombinants are mutually exclusive [34]. This method appears to perform better than
the classical DE [25].
Opposition based differential evolution (ODE)
: DE usually start with some
ran-dom guesses and works with no prior information about the actual optimum solution
[35]. Fast convergence to the optima can be obtained simultaneously by checking the
fitness of the opposite solution [36]. This has proved useful as the initial candidate
solution can be chosen between the better fit options of the guess or opposite guess
[37]. The process can be extended before the birth of each individual of the
popula-tion.
Differential evolution with neighborhood-based mutation:
This is the use of
ex-ploitation in DE which helps the algorithm to search new regions in a
multi-dimensional search space. This variant of DE is effective because of two things.
First-ly, the search algorithm utilizes the initial information and search towards the optima
and lastly, the search algorithm will be very effective in the introduction and
man-agement of information into the population [38]. The idea behind this to prevent the
search from favouring only vectors in the neighbourhood, but to extend the search to
other areas.
Differential evolution with adaptive selection of mutation strategies:
This
vari-ant of DE makes use of the control parameters values and self-adapted trial vector g
eneration strategies to produce new individuals that are candidates for the optimum
solution [27]. This is done by using the historical data and creating patterns that will
generate the solution (unsupervised learning).
information. This helps in the creation of new candidate solutions to facilitate
conver-gence and to discourage arbitrary tuning of the control parameters [26].
Hybrid Differential Evolution Algorithms:
Hybrid models or algorithms in
gen-eral are the combination of two or more parent algorithms to produce another one
(offspring), whereby the outcome (offspring) is expected to be better than the parent
algorithms. This is because; hybrid algorithms are built upon the best features of the
parent algorithms. Hybridisation in DE takes three forms.
•
Hybridisation with other EC algorithms: such as particle swarm optimisation
[39-40], cultural algorithms [41], biogeography-based optimisation [42], earthworm
[43], bacterial foraging optimisation algorithm [44-45], bare bones [46] and
modi-fied bare bones swarm optimizers [47], ant bee colony algorithm [48] and genetic
algorithm [49]. Others are: tissue membrane systems [50], artificial immune
sys-tems [51], firefly algorithm [52], simulated annealing [53], neural networks [54],
bat algorithm [55], krill herd algorithm [56], memetic inspired systems [57],
fire-works optimisation [58], Cuckoo Search algorithm [59] and Grey Wolf optimizer
[60].
•
The use of local search technique (algorithms) in DE to improve the ability of the
DE algorithm to make effective utilization of the information collected and to push
towards obtaining the optimum solution [61]. The local search is usually adapted in
the crossover stage of the DE, thereby increasing the likelihood that the optimal
so-lutions (offspring with high fitness) will be found in small neighbourhood around
the candidate solutions and reduction of fitness function evaluations. Hybridisation
can also be done using neighbourhood search [62], Taguchi operator [63],
cluster-ing [64], shuffled [65] and chaotic local search, Levy flight, and Golden Section
Search [66].
•
Hybridisation with non-Darwinian methods: DE has been hybridized with some
non-evolutionary techniques such as: black hole inspired systems [67] and
gravita-tion search algorithm [68] and radial basis funcgravita-tion response surface [69].
•
Differential Evolution for Discrete and Binary Optimisation: DE was originally
created for real value parameters. Over the years, several researchers have
modi-fied it to be utilized in tackling binary and discrete optimisation problems. This can
be achieved by the following: truncating or approximating the parameter values for
objective function evaluation [70] or discretisation of continuous value parameters
[71], bicriteria [72] and purely binary optimisation [73]. Most applications of DE in
this context are for solving job and machine scheduling problems.
2.4
Major strengths of the differential evolution
DE can be applied to tackle real world problems, which are unimodal/multimodal,
linear/non-linear, differentiable/nondifferentiable convex/non-convex, continuous/
non-continuous and symmetrical/asymmetrical in nature. These are categorized as
follows:
Multiobjective optimisation (MO)
:
Real world problems are often complex
be-cause of the composition of the different variables that are used in modelling them.
These imply some problems have several criteria and objectives, which must be
eval-uated simultaneously in order to obtain the solution [78]. DE has proven to be well
suited for tackling this type of optimisation problem. The most prominent modified
version of DE that is used in solving MO problems are Pareto DE [79] and non-Pareto
DE [80].
Constrained optimisation (CO):
DE is very good at solving real world problems
that come with conditions known as constraints. The most profound constraints are
called the boundary constraint [81] or boundary value problems in numerical analysis
or numerical optimisation and inequality constraints [82].
Large-scale optimisation (LSO):
Most search abilities of EC algorithms failed at
a very high dimension. This is due to, firstly, the complexity of the problem and the
fatigue of the search strategy and secondly, the exponential increase in the solution
space caused by the time it takes for the search to yield an optimum solution. This
problem is present in almost all the EC algorithm of which DE is not an exception.
However, experts in DE have provided means of which DE can be used to solve large
scale optimisations. Some of the surveyed approaches are the fitness function
refine-ment [83], use of chaotic systems and simplex search method [84], co-evolution [85],
self-adaptive method [86], random grouping scheme [87], surrogate-assisted [88] and
hybrid of co-evolution and log-normal self-adaptation [89], fuzzy adaptive method
[90], strategy adaptation [27] and competition based strategy [91].
Optimisation in dynamic and uncertain environments:
EC algorithms generally
suffers from the uncertainties present in the optimisation problems. Those
uncertain-ties can be time, place or measurement indexed. These uncertainuncertain-ties can manifest as
the noisiness of the fitness function, the effect of the computing environment on the
parameters, case of the fitness function being approximated and the optimal nature of
the candidate solution varies over time and location. Researchers have designed
dif-ferent strategies to address these issues in DE environment. Intermittent varying of the
scale parameter and incorporated a very good search method [92], optimisation of the
objective functions that are slow and also changes with time [93] and introduction of
aging mechanism to handle unstable fitness functions [94] are some of the available
strategies.
not limited to the following: fitness sharing [95], clearing [96], crowding [97],
specia-tion [98] and restricted tournament selecspecia-tion [99].
2.5
Challenges and future research areas of differential evolution
Irrespective of the advancement made in the modification of DE, the method is still
faced with some challenges, some of which are presented.
•
DE is still struggling to tackle objective functions that are not linearly separable
[100].
•
DE has been observed to fail to adequately convey the population to large distances
across the solution spaces, especially when clustered population of candidate
solu-tions are encountered [101].
•
Rotation invariance remains an issue [102].
•
DE is often plagued with low convergence rate due to the action of the randomized
mutation operators and competition between the population and its individuals
[103].
•
DE is yet to convincingly prove that it can compute expensive problems better than
other evolutionary computation methods [104].
•
It is still very vague in DE environment; the optimum population size adaptation
strategy to adopt that will yield optimum performance [105].
•
Learning based approaches (supervised, reinforcement and unsupervised learning)
have not been fully incorporated in DE [106].
•
The problem of parameter settings indicates that more research is needed in this
direction [107].
•
The search continues for an EC that can guarantee 100% optimum solution.
•
The following are yet to be fully developed or estimated for DE. They include:
computational complexity, convergence rate estimation, expected first hitting time,
the necessary and sufficient conditions that guarantee convergence and unified
formulation in the theoretical development [107].
•
It cannot be stated, the ranking performance of DE in solving these problems which
include: multiobjective optimisation, constrained optimisation, large-scale
sation, optimisation in dynamic and uncertain environments or multimodal
optimi-sation.
•
Finally, it can be seen that there is no automatic method of selecting a DE variant
for a given problem since studies have shown that DE variants are designed to
im-prove one aspect of DE and as such, may perform very well for a specific type of
problem and perform very poor in others. Fan et al. [108] has proposed an
auto-selection mechanism (ASM) in order to tackle the challenge.
3
DE in Wireless Communications
two or more points, that is, without the aid of wires, cables or any other forms of
elec-trical conductors. The transmitted distance ranges from a few metres to thousands of
kilometres. Wireless communication can be used in radio wireless technology,
cellu-lar telephony, wireless internet access, satellite and broadcast television, wireless
home networking, cordless telephones and others. Wireless communication has
sever-al advantages over wired one. It is cost effective, flexible, convenient, fast, easily
accessible and the probability of maintaining constant connectivity is high. However,
security, coverage and other challenges are some of the issues with wireless
commu-nication.
The problems encountered in wireless communication are often NP hard.
Conse-quently, they are modelled as a constrained optimisation problem, of which
differen-tial evolution (DE) is routinely applied to optimize the objective function resulting
from the problem formulation. Minimisation or maximisation of the objective
func-tion subject to some constraints are usually the main.
A review of previous studies showed that there are six interconnecting areas where
DE has been applied in wireless communications. They are: energy optimisation,
improving quality of service, localisation and coverage area maximisation, updating
mechanism, security application and related field applications.
3.1
Energy optimisation
Energy is required in transmission of data in wireless networks and estimation of
energy consumption is important for network planning [109]. Energy consumption
optimisation is a predictor of overall network performance and remains the most
im-portant constraint. DE has been used to achieve efficient energy optimisation in WSN
[110] and power allocation in orthogonal frequency division multiplexing (OFDM)
systems [111] thereby decreasing the gross impact of the limited available energy
[112].
In order to maintain consistent energy, energy harvesting technology has been
pro-posed to improve network throughput. DE is used to obtain the optimal throughput
that will sustain consistent energy [113] and extend the lifetime of individual nodes in
WSNs [114].
3.2
Quality of service improvement
In improving the quality of network, it is always desirable to optimize the
con-straints that will yield maximum quality of service (QOS). DE has been applied to the
optimisation of network coverage, power consumption, cost and human exposure
minimisation to the network [121-122]. Different examples are given. They are: the
case of heterogenous networks consisting of WiFi access points [123]; multi objective
node deployment to ensure reliable and efficient real time performance [124-125] and
lifetime maximisation [126]; optimum allocation of spectrum in wireless networks
[127] and minimisation of the number of links in WSNs [128].
DE has been applied to minimize the installation cost satisfying QOS constraints
in Wireless Mesh Network (WMN) [129] and minimisation of overall mobility
man-agement cost in wireless cellular networks [130]. Others are the minimisation of
de-sign and transmission costs with the aid of DE [131].
The following QOS constraints were optimised using DE; the bit error rate (BER),
bandwidth, associativity-based routing (ABR), monetary cost and signal to noise ratio
(SNR) [132]. For instance, a hybrid of DE and genetic algorithm was used to
mini-mise the BER and multi-path effect of the channel thereby increasing the convergence
speed [133-134]. Also, DE was used to minimize the BER in Multi-User Multiple
Input Multiple Output (MU-MIMO) [135] and in general, solving the beamforming
problems subjected to different variables and constraints [136]. DE was used in the
optimum allocation of bandwidth in Cellular IP network, thereby improving the QoS
[137].
The consequence of the optimisation is the minimisation of hangovers, that is the
“Ping Pong” effect [138], minimisation of end to end video reconstruction distortion
[139] and resilience strategy which guarantees that a network can withstand the
fail-ure of few a nodes or links. Relay nodes is one of the resilience strategy and DE is
used to find the optimum number of relay nodes that will improve connectivity and
minimize network downtime [140].
Multicast routing is often preferred strategy in quality service delivery, especially
in multichannel multiradio wireless mesh networks. DE has shown to be efficient in
finding the optimal performance in routing [141-142], packet delivery ratio
maximisa-tion [143], delay minimisamaximisa-tion [144] and optimum reassigning vacant channel to
cog-nitive users without network deterioration [145]. Assignment can also take the form of
allocation in download link systems [146].
Transmission rate, transmitter location and network throughput of different
wire-less networks have been optimized using the DE [147]. Application of DE helped in
the optimisation of network throughput in networks with dynamic topological
struc-ture [148].
3.3
Localisation and coverage area maximisation
Localisation in wireless networks often involves the location of sensed data in
wireless sensors and devices. Location information on localisation is crucial in
cover-age, sensor node deployment, target tracking and routing. DE was applied as a
locali-sation algorithm to enhance the quality of information and for convergence purposes
of determining the optimal distances between nodes [154-155]. Location quality can
be enhanced using DE [156-157] and specifically in base stations (BS) [158]. Apart
from accuracy of location estimation, DE has shown to be useful in reducing the time
complexity, thereby leading to localisation error reduction [159-160]. A further
reduc-tion of the localisareduc-tion error was achieved by the hybrid of DE and Monte Carlo
local-isation algorithm. This is a case where the sample weight is taken as the objective
function [161]. A hybrid of DE and genetic algorithm has been used as a localisation
algorithm in the estimation of the location of nodes in WSN [162]. Moreover,
locali-sation by using DE can be improved by adaptive controls over the parameters to
en-sure adequate tuning [163].
Generally, coverage problems in WSN are modelled as optimisation problem and
can be solved using evolutionary algorithms such as DE [164]. DE is used in solving
connection based localisation problem features prominently in wireless sensor
net-works where connections can be modelled as a nonconvex or non-convex
optimisa-tion problem which can easily be handled using DE [165].
DE has been used in finding the minimum subset of sensor nodes to cover all the
targets in wireless multimedia sensor networks [166] and hence solving the targets
coverage problem [167-168] and nudge redundant active nodes into sleep mode [169]
or reduction of number of individual nodes which participate in non-dominated
solu-tion sorting [170]. Also available is the use of DE to optimize sensor nodes over
di-verse area shape, thereby increasing the coverage area [171]. Coverage radius and
load balancing were optimized using DE which acts as the gateway deployment
algo-rithm [172]. DE was used as deployment algoalgo-rithm in optimisation of variables
de-fined for directional WSNs [173].
3.4
Updating mechanism
DE algorithm can be applied as position updating mechanism where candidate
po-sitions learn from a large diversified search region such as online heuristic searching
[174] and search equations for the purpose of reliable data collection [175]. The
out-come is to determine the optimum path that satisfies the different quality of service
(QOS) constraints in Mobile Ad Hoc Networks (MANETs) [176]. DE has been found
to be a crossover strategy used as a search tool in solving optimisation problems in
WSNs and superior to genetic algorithm and particle swarm optimisation [177].
3.5
Security
Security issues are one of several issues facing WSN and intrusion detection
sys-tem (IDS) is indispensable in the security of WSN. The aim of IDS is to detect
mali-cious activities that affect the predefined network protocols. The multi-dimensional
nature of the datasets of IDS causes data redundancy which leads to poor performance
and slow speed. In order to address the data dimension issue, feature selections are
often used in IDS which can be effectively optimised by the application of DE [179].
Apart from IDS, trust interference is another method of addressing security issues in
WSN. DE was applied to compute trust values for each individual node in the WSN
[180].
Another aspect of the security issues in WSN is the data aggregation caused by an
enormous connectivity from different devices connected to the network. As a result,
the network is vulnerable to security threats at the aggregated nodes. To solve the
problem, DE was used to compute the trusted aggregated node among multiple nodes
[181]. DE was combined with artificial immune system in the optimisation of the
distribution and effectiveness of the detector generator in WSN intrusion detection
[182].
The strategy of maintaining network reliability and at the same time achieving
pri-vacy preservation in WMAN can be handled using IoT-oriented offload method. DE
can be used to optimize the variables while preserving privacy [183]. Random flipped
is often recommended in preventing security attacks of WSN on an insecure link.
Optimum flipping can be obtained using DE to minimize the fusion error and ensuring
secure data transmission [184]. DE was applied to obtain optimal power schedule in
wireless networks thereby, minimizing the occurrence of the denial of service (DoS)
attacks [185].
3.6
Related field applications
DE is applied when the studied problem is modelled as a network with given
objec-tive function to be minimised or maximised. Another aspect is when DE is combined
with other methods and applied in fields related to wireless communication. DE was
applied to determine the optimal design for the appropriate pipes that fits the network
distribution in water distribution system subject to cost and total loss constraints
[186].
DE was applied to predict gas concentration while WSN systems were used to
col-lect the data [187]. DE was used in energy optimisation of environmental driven WSN
[188]. DE is used in path planning for unmanned underwater vehicle's (UUV) [189].
4
Conclusion
of DE have been used in wireless communication. Two major strengths of DE are
efficient handling of multi-objective and multimodal optimisations. As seen in the
review, most of the optimisation problems in wireless networks are multi-objective
and multimodal in nature, of which DE was applied to obtain the desired solutions. It
appears that coverage area maximisation and energy consumption minimisation are
the two major areas where Differential Evolution is applied in wireless networks and
communications, which was part of the submission of [190]. The networks are usually
modelled as a multi-objective optimisation problem where variables are optimised
using some constraints. The variables can be energy efficiency, coverage, resource
allocation and so on, while the constraints can be in the form of link conflict and
inter-ference [191]. Thereafter, evolutionary algorithms, DE in this case are applied to
solve the optimisation problem subject to the given constraint. Different research
paths on the use of DE in wireless networks can be followed.
5
Acknowledgement
The authors are grateful to Covenant University for providing an enabling
envi-ronment for this research.
6
References
[1]Fogel, D.B. (1995). Evolutionary Computation: Toward a New Philosophy of Machine In-telligence. IEEE Press, Piscataway, NJ.
[2]Bäck, T., Fogel, D. B. & Michalewicz, Z. (Eds), (1997). Handbook of Evolutionary Com-putation. Oxford University Press.
[3]De Jong, K.A. (2006). Evolutionary Computation: A Unified Approach. MIT Press, Cam-bridge MA.
[4]Eiben, A.E. & Smith, J.E. (2003). Introduction to Evolutionary Computing. Springer. [5]Fogel, L.J., Owens, A.J. & Walsh, M.J. (1966). Artificial Intelligence through Simulated
Evolution, New York: John Wiley.
[6]Rechenberg, I. (1971). Evolutionsstrategie - Optimierung Technischer Systeme nach Prin-zipien der Biologischen Evolution. PhD thesis. https://doi.org/10.1002/fedr.491086050 6
[7]Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.
[8]Koza, J.R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Evolution. MIT Press, Massachusetts.
[9]Diaz Ochoa, J.G. (2018). Elastic Multi-scale Mechanisms: Computation and Biological Evolution. J. Molec. Evol. 86 (1): 47-57.
[10]Jamshidi M. (2003). Tools for intelligent control: fuzzy controllers, neural networks and genetic algorithms. Philos. Trans. Royal Soc. A. 361 (1809): 1781-808.
[11]Danchin, A. (2008). Bacteria as computers making computers. FEMS Microbiol. Review, 33 (1): 3-26.
[13]Ighravwe, D.E., Oke, S.A. & Adebiyi, K.A. (2018). An enhanced reliability-oriented work-force planning model for process industry using combined fuzzy goal programming and differential evolution approach. J. Ind. Engine. Int., 14(1): 185-212. https://doi.org/10. 1007/s40092-017-0223-9
[14]Ighravwe, D.E. & Oke, S.A. (2016). A machine survival time-based maintenance work-force allocation model for production systems. Afr. J. Sci. Tech. Innovat. Develop., 8(5-6): 457-466.
[15]Adebiyi, A.A. & Ayo, C.K. (2015). Portfolio selection problem using generalized differen-tial evolution 3. Appl. Math. Sci., 9(41-44): 2069-2082.
[16]Storn, R. & Price, K.V. (1995). Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces, ICSI, USA, Tech. Rep. TR-95-012. [Online]. Available: http://icsi.berkeley.edu/∼storn/litera.html.
[17]Storn, R. & Price, K.V. (1996). Minimizing the real functions of the ICEC 1996 contest by differential evolution. In Proc. IEEE Congress Evol. Comput., 842-844. https://doi.org /10.1109/icec.1996.542711
[18]Price, K.V. (1997). Differential evolution vs. the functions of the 2nd ICEO. In Proc. IEEE Congress Evol. Comput., 153–157.
[19]Price, K.V. & Storn, R. (1997). Differential evolution: A simple evolution strategy for fast optimization. Dr. Dobb’s J., 22(4): 18-24.
[20]Eltaeib, T. & Mahmood, A. (2018). Differential evolution: A survey and analysis. Appl. Sci., 8(10): Art. no. 1945.
[21]Javaid, N. (2019). Differential evolution: An updated survey. Adv. Intel. Syst. Comput., 772: 681-691.
[22]Nelder, J.A. & Mead, R. (1965). A simplex method for function minimization. Computer J., 7: 308-313. https://doi.org/10.1093/comjnl/7.4.308
[23]Price, W.L. (1977). Global optimization by controlled random search, Computer J., 20(4): 367-370.
[24]Das, S. & Suganthan, P.N. (2011). Differential evolution: A survey of the state-of-the-art. IEEE Trans. Evol. Comput., 15 (1): 4-31.
[25]Das, S., Abraham, A., Chakraborty, U.K. & A. Konar, A. (2009). Differential evolution us-ing a neighborhood-based mutation operator. IEEE Trans. Evol. Comput., 13(3): 526–553.
https://doi.org/10.1109/tevc.2008.2009457
[26]Zhang, J. & Sanderson, A.C. (2009). JADE: Adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput., 13 (5): 945-958. https://doi.org/10.1109 /tevc.2009.2014613
[27]Qin, A.K., Huang, V.L. & Suganthan, P.N. (2009). Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput., 13(2): 398-417. https://doi.org/10.1109/tevc.2008.927706
[28]Liu, J. & Lampinen, J. (2002). On setting the control parameters of the differential evolu-tion method. In: Matoušek, R. & Ošmera, P. (eds.) Proc. Mendel, 8th Int. Conf. Soft Com-put., 11-18.
[29]Liu, J. & Lampinen, J. (2002). Adaptive parameter control of differential evolution. Ma-toušek, R. & Ošmera, P. (Eds.) Proc. Mendel, 8th Int. Conf. Soft Comput., 19-26.
[30]Gämperle, R., Müller, S.D. & Koumoutsakos, P. (2002). A parameter study for differential evolution. In Proc. WSEAS Int. Conf. Adv. Intel. Syst. Fuzzy Syst. Evol. Comput., 293-298.
[32]Vaishali, Sharma, T.K., Abraham, A. & Rajpurohit, J. (2018). Enhanced asynchronous dif-ferential evolution using trigonometric mutation. Adv. Intel. Syst. Comput., 614: 386-397. [33]Price, K.V. (1999). An introduction to differential evolution, In New Ideas in
Optimiza-tion, D. Corne, M. Dorigo, & V. Glover, Eds. London, U.K.: McGraw-Hill, 79–108. [34]Price, K.V., Storn, R. & Lampinen, J. (2005). Differential Evolution—A Practical
Ap-proach to Global Optimization. Berlin, Germany: Springer.
[35]Tizhoosh, H.R. (2005). Opposition-Based Learning: A New Scheme for Machine Intelli-gence, Int. Conf. on Comput. Intel. for Model. Control and Auto.- I, 695-701, Vienna, Austria.
[36]Rahnamayan, R.S., Tizhoosh, H.R. & Salama, M.M.A. (2008). Opposition-based differen-tial evolution. IEEE Trans. Evol. Comput., 12 (1): 64-79. https://doi.org/10.1109/te vc.2007.894200
[37]Tizhoosh, H.R. (2006). Opposition-based reinforcement learning, J. Adv. Comput. Intel. Intel. Inform., 10: Article: 3.
[38]Mezura-Montes, E., Vel´azquez-Reyes, J. & Coello, C.A. (2006). A comparative study of differential evolution variants for global optimization, In Proc. Conf. Genetic Evol. Com-put., 485-492. https://doi.org/10.1145/1143997.1144086
[39]Xin, B., Chen, J., Peng, Z.H. & Pan, F. (2010). An adaptive hybrid optimizer based on par-ticle swarm and differential evolution for global optimization. Sci. China, Series F: Info. Sci., 53(5): 980-989. https://doi.org/10.1007/s11432-010-0114-9
[40]Xin, B., Chen, J., Zhang, J., Fang, H. & Peng, Z.-H. (2012). Hybridizing differential evolu-tion and particle swarm optimizaevolu-tion to design powerful optimizers: A review and taxon-omy. IEEE Trans. Syst. Man Cyber. Part C: Appl. Rev., 42 (5): 744-767.
https://doi.org/10.1109/tsmcc.2011.2160941
[41]Awad, N.H., Ali, M.Z., Suganthan, P.N. & Reynolds, R.G. (2017). CADE: A hybridization of Cultural Algorithm and Differential Evolution for numerical optimization. Info. Sci., 378: 215-241. https://doi.org/10.1016/j.ins.2016.10.039
[42]Gong, W., Cai, Z. & Ling, C.X. (2011). DE/BBO: A hybrid differential evolution with bi-ogeography-based optimization for global numerical optimization. Soft Comput.,15(4): 645-665. https://doi.org/10.1007/s00500-010-0591-1
[43]Javaid, N., Ullah, I., Zarin, S.S., Kamal, M., Omoniwa, B. & Mateen, A. (2019). Differen-tial-evolution-earthworm hybrid meta-heuristic optimization technique for home energy management system in smart grid. Adv. Intel. Syst. Comput., 773: 15-31. https: //doi.org/10.1007/978-3-319-93554-6_2
[44]Biswas, A., Dasgupta, S., Das, S. & Abraham, A. (2007). A synergy of differential evolu-tion and bacterial foraging optimizaevolu-tion for global optimizaevolu-tion. Neural Network World, 17(6): 607-626.
[45]Passino, K.M. (2002). Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst. Mag., 22(3): 52-67. https://doi.org/10.1109/mcs.2002.1004010
[46]Omran, M.G.H., Engelbrecht, A.P. & Salman, A. (2009). Bare bones differential evolution. Euro. J. Operat. Res., 196(1): 128-139.
[47]Zhang, Q., Zhang, H., Yang, B. & Hu, Y. (2018). Gaussian Cauchy differential evolution for global optimization. Comm. Comput. Info. Sci., 888: 166-182
[48]Jadon, S.S., Tiwari, R., Sharma, H. & Bansal, J.C. (2017). Hybrid Artificial Bee Colony algorithm with Differential Evolution. Appl. Soft Comput. J., 58: 11-24. https://doi.org/10. 1016/j.asoc.2017.04.018
[50]Zhang, G., Cheng, J., Gheorghe, M. & Meng, Q. (2013). A hybrid approach based on dif-ferential evolution and tissue membrane systems for solving constrained manufacturing pa-rameter optimization problems. Appl. Soft Comput. J., 13(3): 1528-1542. https://doi.org/ 10.1016/j.asoc.2012.05.032
[51]Lin, Q., Zhu, Q., Huang, P., Chen, J., Ming, Z. & Yu, J. (2015). A novel hybrid multi-objective immune algorithm with adaptive differential evolution. Comp. Oper. Res., 62: 95-111. https://doi.org/10.1016/j.cor.2015.04.003
[52]Abdullah, A., Deris, S., Mohamad, M.S. & Hashim, S.Z.M. (2012). A new hybrid firefly algorithm for complex and nonlinear problem. Adv. Intel. Soft Comput., 151: 673-680.
https://doi.org/10.1007/978-3-642-28765-7_81
[53]Addawe, R.C., Addawe, J.M., Sueno, M.R.K. & Magadia, J.C. (2017). Differential evolu-tion-simulated annealing for multiple sequence alignment. J. Physics: Conf. Series, 893(1): 012061. https://doi.org/10.1088/1742-6596/893/1/012061
[54]Wang, L., Zeng, Y. & Chen, T. (2015). Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Syst. Appl., 42(2): 855-863. https://doi.org/10.1016/j.eswa.2014.08.018
[55]Fister Jr., I., Fister, D. & Yang, X.-S. (2013). A hybrid bat algorithm. Electrotechnical Re-view, 80(1-2): 1-7.
[56]Wang, G.-G., Gandomi, A.H., Alavi, A.H. & Hao, G.-S. (2014). Hybrid krill herd algo-rithm with differential evolution for global numerical optimization. Neural Comput. Appl., 25(2): 297-308. https://doi.org/10.1007/s00521-013-1485-9
[57]Wu, X. & Che, A. (2019). A memetic differential evolution algorithm for energy-efficient parallel machine scheduling. Omega, 82: 155-165. https://doi.org/10.1016/ j.omega.2018.01.001
[58]Zheng, Y.-J., Xu, X.-L., Ling, H.-F. & Chen, S.-Y. (2015). A hybrid fireworks optimiza-tion method with differential evoluoptimiza-tion operators. Neurocomputing, 148: 75-82.
https://doi.org/10.1016/j.neucom.2012.08.075
[59]Lin, H. & Siu, S. (2018). A Hybrid Cuckoo Search and Differential Evolution Approach to Protein–Ligand Docking. Int. J. Molec. Sci., 19(10): Article 3181. https://doi.org/ 10.3390/ijms19103181
[60]Gupta, S. & Deep, K. (2019). Hybrid Grey Wolf Optimizer with mutation operator. Adv. Intel. Syst. Comput., 817: 961-968.
[61]Noman, N. & Iba, H. (2008). Accelerating differential evolution using an adaptive local
search. IEEE Trans. Evol. Comput., 12(1): 107-125.
https://doi.org/10.1109/tevc.2007.895272
[62]Yang, Z., Tang, K. & Yao, X. (2007). Differential evolution for high dimensional function optimization. In Proc. IEEE Congress Evol. Comput., 3523–3530.
[63]Yildiz, A.R. (2013). Hybrid Taguchi-differential evolution algorithm for optimization of multi-pass turning operations. Appl. Soft Comput. J., 13(3): 1433-1439. https://doi.org/ 10.1016/j.asoc.2012.01.012
[64]Cai, Z., Gong, W., Ling, C.X. & Zhang, H. (2011). A clustering-based differential evolu-tion for global optimizaevolu-tion. Appl. Soft Comput. J., 11(1): 1363-1379. https://doi.org/ 10.1016/j.asoc.2010.04.008
[65]Srinivasa Reddy, A. & Vaisakh, K. (2013). Shuffled differential evolution for large scale economic dispatch. Elect. Power Syst. Res., 96: 237-245. https://doi.org/10.1016/ j.epsr.2012.11.010
[67]Sharma, P., Sharma, H., Kumar, S. & Sharma, K. (2019). Black-hole gbest differential evolution algorithm for solving robot path planning problem. Adv. Intel. Syst. Comput., 741: 1009-1022. https://doi.org/10.1007/978-981-13-0761-4_95
[68]Li, X., Yin, M. & Ma, Z. (2011). Hybrid differential evolution and gravitation search algo-rithm for unconstrained optimization. Int. J. Phys. Sci., 6(25): 5961-5981.
[69]Deng, K. & Chen, H. (2017). Hybrid Optimization Algorithm based on Differential Evolu-tion and RBF Response Surface. Chinese J. Theo. Appl. Mech., 49 (2): 441-455.
[70]Lampinen, J. & Zelinka, I. (1999). Mixed integer-discrete-continuous optimization with differential evolution. In Proc. of Mendel, 5th Int. Conf. on Soft Comput., 71-76.
[71]Tasgetiren, M.F., Liang, Y.C., Sevkli, M. & Gencyilmaz, G. (2004). Differential Evolution Algorithm for Permutation Flowshop Sequencing Problem with Makespan Criterion, 4th Int. Symposium on Intel. Manufac. Syst., Sakarya, Turkey, 442-452. https://doi.org/10. 1007/978-3-540-28646-2_38
[72]Pan, Q.K., Wang, L. & Qian, B. (2009). A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems. Comp. Oper. Res., 36: 2498-2511.
https://doi.org/10.1016/j.cor.2008.10.008
[73]Pampara, G., Engelbrecht, A.P. & Franken, N. (2006). Binary differential evolution. In Proc. IEEE Congress Evol. Comput., 1873-1879.
[74]Lampinen, J. (1999). Differential evolution: New naturally parallel approach for engineer-ing design optimization, in Developments in Computational Mechanics with High Perfor-mance Computing, B. H. V. Topping, Ed. Edinburgh, U.K.: Civil-Comp Press, 217-228.
https://doi.org/10.4203/ccp.57.11.2
[75]Tasoulis, D.K., Pavlidis, N.G., Plagianakos, V.P. & Vrahatis, M.N. (2004). Parallel differ-ential evolution. Proc. IEEE Congress Evol. Comput., 2023–2029. https://doi.org/10. 1109/cec.2004.1331145
[76]Yoshida, H. & Fukuyama, Y. (2018). Parallel multi-population differential evolutionary particle swarm optimization for voltage and reactive power control. IEEJ Trans. Power and Energy, 138 (2): 116-123. https://doi.org/10.23919/sice.2017.8105566
[77]Pedroso, D.M., Bonyadi, M.R. & Gallagher, M. (2017). Parallel evolutionary algorithm for single and multi-objective optimisation: Differential evolution and constraints handling. Appl. Soft Comput. J., 61: 995-1012. https://doi.org/10.1016/j.asoc.2017.09.006
[78]Madavan, N.K. (2002). Multiobjective optimization using a pareto differential evolution approach. Congress on Evol. Comput., Piscataway, New Jersey, 2: 1145-1150.
[79]Abbass, H.A. & Sarker, R. (2002). The Pareto differential evolution algorithm. Interna-tional J. Artif. Intel. Tools, 11(4): 531-552. https://doi.org/10.1142/s0218213002 001039
[80]Babu, B.V. & Jehan, M.M.L. (2003). Differential evolution for multiobjective optimiza-tion. In Proc. IEEE Congress Evol. Comput., 4: 2696-2703.
[81]Storn, R. (1996). On the usage of differential evolution for function optimization, in Proc. North Am. Fuzzy Inform. Process. Soc., 519-523.
[82]Deb, K. (2000). An efficient constraint handling method for genetic algorithms. Comp. Meth. Appl. Mech. Engine., 186(2-4): 311-338.
[83]Noman, N. & Iba, H. (2005). Enhancing differential evolution performance with local search for high dimensional function optimization. In Proc. Conf. Genetic Evol. Comput., 967-974. https://doi.org/10.1145/1068009.1068174
[85]Potter, A.M. & De Jong, K.A. (1994). A cooperative co-evolutionary approach to function optimization, Proc. of the 3rd Int. Conf. Parallel Problem Solving from Nature, 249–25, Springer-Verlag.
[86]Yang, Z., He, J. & Yao, X. (2007). Making a difference to differential evolution, in Ad-vances in Metaheuristics for Hard Optimization, Michalewicz, Z. and Siarry, P. Eds., Ber-lin, Germany: Springer, 415-432.
[87]Yang, Z., Tang, K. & Yao, X. (2008). Large scale evolutionary optimization using cooper-ative coevolution, Info. Sci., 178 (15): 2985-2999. https://doi.org/10.1016/j.ins.2008 02.017
[88]Su, G. (2008). Gaussian process assisted differential evolution algorithm for computation-ally expensive optimization problems, Pacific-Asia Workshop on Comput. Intel. & Ind. Appl., 1: 272-276. https://doi.org/10.1109/paciia.2008.184
[89]Zamuda, A., Brest, J., Boskovic, B. & Zumer, V. (2008). Large Scale Global Optimization using Differential Evolution with self-adaptation and cooperative co-evolution. In Proc. IEEE Congress Evol. Comput., 3718-3725. https://doi.org/10.1109/cec.2008.4631301
[90]Liu, J. & Lampinen, J. (2005). A fuzzy adaptive differential evolution algorithm. Soft Computing, 9 (6): 448-462. https://doi.org/10.1007/s00500-004-0363-x
[91]Ge, Y.-F., Yu, W.-J., Zhan, Z.-H. & Zhang, J. (2018). Competition-Based Distributed Dif-ferential Evolution. In Proc. IEEE Congress Evol. Comput., Art. no. 8477758.
[92]Das, S., Konar, A. & Chakraborty, U. (2005). Improved differential evolution algorithms for handling noisy optimization problems. In Proc. IEEE Congress Evol. Comput., 2: 1691-1698. https://doi.org/10.1109/cec.2005.1554892
[93]Mendes, R. & Mohais, A.S. (2005). DynDE: A differential evolution for dynamic optimi-zation problems. In Proc. IEEE Congress Evol. Comput., 2: 2808-2815. https://doi. org/10.1109/cec.2005.1555047
[94]Brest, J., Zamuda, A., Boskovic, B., Maucec, M.S. & Zumer, V. (2009). Dynamic optimi-zation using self-adaptive differential evolution. In Proc. IEEE Congress Evol. Comput., 415-422. https://doi.org/10.1109/cec.2009.4982976
[95]Dick, G. & Whigham, P. (2008). Spatially-structured sharing technique for multimodal problems. J. Comp. Sci. Technol., 23: 64-76. https://doi.org/10.1007/s11390-008-9110-6
[96]Pétrowski, A. (1996). A clearing procedure as a niching method for genetic algorithms. In Proc. IEEE Congress Evol. Comput., New York, USA, 798–803.
[97]Thomsen, R. (2004). Multimodal optimization using crowding-based differential evolu-tion. In Proc. IEEE Congress Evol. Comput., 1382-1389.
[98]Li, J.-P., Balazs, M.E, Parks, G.T. & Clarkson, P.J. (2002). A species conserving genetic algorithm for multimodal function optimization. Evol. Comput., 10(3): 207-234. https://doi.org/10.1162/106365602760234081
[99]Qu, B.Y. & Suganthan, P.N. (2010). Novel multimodal problems and differential evolution with ensemble of restricted tournament selection. In Proc. IEEE Congress Evol. Comput., 3480–3486. https://doi.org/10.1109/cec.2010.5586341
[100]Hansen, N. & Kern, S. (2004). Evaluating the CMA evolution strategy on multimodal test functions. In Proc. 8th Int. Conf. Parallel Problem Solving from Nature, Berlin, Germany, 282–291. https://doi.org/10.1007/978-3-540-30217-9_29
[101]Langdon, W.B. & Poli, R. (2002). Foundations of Genetic Programming, New York: Springer-Verlag.
[103]Cui, L., Huang, Q., Li, G., Yang, S., Ming, Z., Wen, Z., Lu, N. & Lu, J. (2018). Differen-tial evolution algorithm with tracking mechanism and backtracking mechanism. IEEE Ac-cess, 6: 44252-44267. https://doi.org/10.1109/access.2018.2864324
[104]He, Y.-C., Wang, X.-Z., Liu, K.-Q. & Wang, Y.-Q. (2010). Convergent analysis and algo-rithmic improvement of differential evolution. J. Software, 21(5): 875-885.
[105]Poikolainen, I. & Neri, F. (2013). Differential evolution with concurrent fitness based local search. In Proc. IEEE Congress Evol. Comput., 384-391. https://doi.org/10.1109/cec.2013. 6557595
[106]Mallipeddi, R. & Lee, M. (2015). An evolving surrogate model-based differential evolu-tion algorithm. Appl. Soft Comput. J., 34: 770-787. https://doi.org/10.1016/j.asoc. 2015.06.010
[107]Das, S., Mullick, S.S. & Suganthan, P.N. (2016). Recent advances in differential evolution – An updated survey. Swarm & Evol. Comput., 27: 1-30. https://doi.org/10.1016/j.swevo. 2016.01.004
[108]Fan, Q., Yan, X. & Zhang, Y. (2018). Auto-selection mechanism of differential evolution algorithm variants and its application. Euro. J. Operat. Res., 270 (2): 636-653.
https://doi.org/10.1016/j.ejor.2017.10.013
[109]Céspedes-Mota, A., Castañón, G., Martínez-Herrera, A.F. & Cárdenas-Barrón, L.E. (2016). Optimization of the distribution and localization of wireless sensor networks based on differential evolution approach. Math. Probl. Engine., 2016: Art. no. 7918581.
https://doi.org/10.1155/2016/7918581
[110]Kamal, A., Warip, M.N.M., Elshaikh, M. & Badlishah, R. (2016). Differential evolution (DE) algorithm to optimize Berkeley-MAC protocol for wireless sensor network (WSN). J. Theo. Appl. Info. Tech., 89(2): 314-319.
[111]Zhang, X. & Zhang, X. (2016). Population-adaptive differential evolution-based power al-location algorithm for cognitive radio networks. Eurasip J. Wireless Comm. Network., 2016(1): Article number 219. https://doi.org/10.1186/s13638-016-0722-1
[112]Lin, C.-C., Tsai, C.-T., Deng, D.-J., Tsai, I.-H. & Jhong, S.-Y. (2017). Minimizing elec-tromagnetic pollution and power consumption in green heterogeneous small cell network deployment. Computer Networks, 129: 536-547. https://doi.org/10.1016/j.comnet. 2017.05.023
[113]Liu, Y., Yang, Z., Yu, R., Xiang, Y. & Xie, S. (2015). An efficient MAC protocol with adaptive energy harvesting for machine-to-machine networks. IEEE Access, 3: 358-367.
https://doi.org/10.1109/access.2015.2421517
[114]Rodway, J. & Musilek, P. (2017). Harvesting-aware energy management for environmen-tal monitoring WSN. Energies, 10(5): Article number 607. https://doi.org/10. 3390/en10050607
[115]Sumithra, S. & Victoire, T.A. (2015). Differential evolution algorithm with diversified vi-cinity operator for optimal routing and clustering of energy efficient wireless sensor net-works. Scient. World J., 2015: Art. no. 729634. https://doi.org/10.1155/2015/729634
[116]Rajendra Prasad, D., Naganjaneyulu, P.V. & Satya Prasad, K. (2016). Energy efficient clustering in multi-hop wireless sensor networks using differential evolutionary MOPSO. Brazil. Arch. Biol. Technol., 59: Art. no. e161011. https://doi.org/10.1590/1678-4324-2016161011
[117]Mittal, N., Singh, U. & Sohi, B.S. (2017). A Novel Energy Efficient Stable Clustering Ap-proach for Wireless Sensor Networks. Wireless Pers. Comm., 95(3): 2947-2971.
[118]Rajendra Prasad, D., Naganjaneyulu, P.V. & Satya Prasad, K. (2017). A Hybrid Swarm Optimization for Energy Efficient Clustering in Multi-hop Wireless Sensor Network. Wireless Pers. Commun., 94(4): 2459-2471. https://doi.org/10.1007/s11277-016-3562-8
[119]Potthuri, S., Shankar, T. & Rajesh, A. (2018). Lifetime Improvement in Wireless Sensor Networks using Hybrid Differential Evolution and Simulated Annealing (DESA). Ain Shams Engine. J., 9(4): 655-663. https://doi.org/10.1016/j.asej.2016.03.004
[120]Goudos, S.K., Deruyck, M., Plets, D., Martens, L. & Joseph, W. (2017). Optimization of Power Consumption in 4G LTE Networks Using a Novel Barebones Self-adaptive Differ-ential Evolution Algorithm. Telecom. Syst. 66(1): 109-120. https://doi.org/10.1007/s 11235-017-0279-2
[121]Liu, N., Plets, D., Goudos, S.K., Martens, L. & Joseph W. (2015). Multi-objective network planning optimization algorithm: human exposure, power consumption, cost, and capacity. Wireless Networks, 21(3): 841-857. https://doi.org/10.1007/s11276-014-0822-y
[122]Nekooei, S.M., Chen, G. & Rayudu, R.K. (2017). Automatic design of fuzzy logic control-lers for medium access control in wireless body area networks – An evolutionary ap-proach. Appl. Soft Comput. J., 56: 245-261. https://doi.org/10.1016/j.asoc.2017.02.022
[123]Goudos, S.K., Plets, D., Liu, N., Martens, L. & Joseph, W. (2015). A multi-objective ap-proach to indoor wireless heterogeneous networks planning based on biogeography-based optimization. Computer Networks, 91: 564-576. https://doi.org/10.1016/j. comnet.2015.08.037
[124]Wang, L. An, L., Ni, H.Q., Ye, W., Pardalos, P.M. & Fei, M.R. (2016). Pareto-based mul-ti-objective node placement of industrial wireless sensor networks using binary differential
evolution harmony search. Adv. Manufacturing, 4(1): 66-78.
https://doi.org/10.1007/s40436-016-0135-8
[125]Cao, B., Zhao, J., Yang, P., Lv, Z., Liu, X., Kang, X., Yang, S., Kang, K. & Anvari-Moghaddam, A. (2018). Distributed parallel cooperative coevolutionary multi-objective large-scale immune algorithm for deployment of wireless sensor networks. Future Gen. Comput. Syst., 82: 256-267. https://doi.org/10.1016/j.future.2017.10.015
[126]Ayinde, B.O. & Hashim, H.A. (2018). Energy-Efficient Deployment of Relay Nodes in Wireless Sensor Networks Using Evolutionary Techniques. Int. J. Wireless Info. Net-works, 25(2): 157-172. https://doi.org/10.1007/s10776-018-0388-1
[127]Huang, L., Liu, J. & Guo, L. (2018). A hybrid mutation artificial bee colony algorithm for spectrum sharing. Int. J. High Perf. Comput. Network., 12(3): 299-306.
https://doi.org/10.1504/ijhpcn.2018.10016377
[128]Khedher, M., Liouane, H. & Douik, A. (2018). Optimized minimum spanning tree for bor-der nodes selection in wireless sensor networks. 15th International Multi-Conference on Systems, Signals and Devices, Art. no. 8570484, 660-665. https://doi.org/10.1109/ssd. 2018.8570484
[129]Merlin Sheeba, G. & Nachiappan, A. (2016). Fuzzy differential evolution based gateway placements in WMN for cost optimization. Adv. Intel. Syst. Comput., 385: 137-145.
https://doi.org/10.1007/978-3-319-23258-4_13
[130]Swayamsiddha, S., Parija, S., Sahu, P.K. & Singh, S.S. (2017). Optimal reporting cell planning with binary differential evolution algorithm for location management problem. Int. J. Intel. Syst. Appl., 9(4): 23-31. https://doi.org/10.5815/ijisa.2017.04.03
[131]Merlin Sheeba, G. & Nachiappan, A. (2017). Performance evaluation of fuzzy DE based node placement in WMN. J. Engine. Research, 5(4): 106-120.
het-erogeneous wireless networks. Sadhana – Acad. Proc. Engine. Sci., 41(7): 727-753.
https://doi.org/10.1016/j.neucom.2016.08.136
[133]Chiu, C.-C., Chen, C.-H., Cheng, Y.-T., Lee, Y.-L., & Chou, Y.-K. (2018). Beamforming techniques at both transmitter and receiver for indoor wireless communication. J. Appl. Sci. Engine., 21(3): 407-412.
[134]Yu, G., Ma, H. & Witarsyah, D. (2018). Optimal path selection algorithm for mobile bea-cons in sensor network under non-dense distribution. Open Physics, 16(1): 1066-1075.
https://doi.org/10.1515/phys-2018-0127
[135]Chiu, C.-C., Lai, G.-D. & Cheng, Y.-T. (2018). Self-adaptive dynamic differential evolu-tion applied to BER reducevolu-tion with beamforming techniques for ultra wideband MU-MIMO systems. Prog. Electromag. Res. 87: 187-197. https://doi.org/10.2528/pierc 18082302
[136]Chiu, C.C., Tong, Y.X. & Cheng, Y.T. (2019). Comparison of self-adaptive dynamic dif-ferential evolution and particle swarm optimization for smart antennas in wireless commu-nication. Int. J. Commun. Syst., Art. no. e3941. https://doi.org/10.1002/dac.3941
[137]Afzal, Z., Shah, P.A., Awan, K.M. & Zahoor-ur-Rehmanb. (2019). Optimum bandwidth allocation in wireless networks using differential evolution. J. Ambient Intel. Hum. Com-put., 10(4): 1401-1412. https://doi.org/10.1007/s12652-018-0858-4
[138]Goudarzi, S., Hassan, W.H., Anisi, M.H. & Soleymani, S.A. (2017). MDP-Based Network Selection Scheme by Genetic Algorithm and Simulated Annealing for Vertical-Handover in Heterogeneous Wireless Networks. Wireless Pers. Commun., 92(2): 399-436.
[139]Zhao, K. & Sun, Y. (2017). Genetic-optimization framework for SVC transmission based on partial cooperative communication. J. Syst. Engine. Electro., 28(5): Art. no. 8240030, 861-870. https://doi.org/10.1007/s11277-016-3549-5
[140]Sapre, S. & Mini, S. (2018). Moth Flame Based Optimized Placement of Relay Nodes for Fault Tolerant Wireless Sensor Networks, In Proc. 9th ICCCNT, Art. no. 8494123.
https://doi.org/10.1109/icccnt.2018.8494123
[141]Chakraborty, D. (2015). I-QCA: An intelligent framework for quality of service multicast routing in multichannel multiradio wireless mesh networks. Ad Hoc Networks, 33: 221-232. https://doi.org/10.1016/j.adhoc.2015.05.007
[142]Chakraborty, D. & Debbarma, K. (2017). Q-CAR: an intelligent solution for joint QoS multicast routing and channel assignment in multichannel multiradio wireless mesh net-works. Appl. Intel., 47(1): 13-27. https://doi.org/10.1007/s10489-016-0871-2
[143]You, K., Yang, W., Yuan, X. & Wang, Y. (2018). Differentiated services routing protocol of WMSNs for underground coal mines. J. Huazhong Uni. Sci. Technol., 46(9), 1-8. [144]Murugeswari, R. & Radhakrishnan, S. (2016). Discrete multi-objective differential
evolu-tion algorithm for routing in wireless mesh network. Soft Computing, 20(9): 3687-3698.
https://doi.org/10.1007/s00500-015-1730-5
[145]Anumandla, K.K., Peesapati, R. & Sabat, S.L. (2015). Field programmable gate array im-plementation of spectrum allocation technique for cognitive radio networks. Comp. Elect. Engine., 42: 178-192. https://doi.org/10.1016/j.compeleceng.2014.07.013
[146]Sharma, N. & Anpalagan, A. (2015). Differential evolution aided adaptive resource alloca-tion in OFDMA systems with proporalloca-tional rate constraints. Appl. Soft Comput. J., 34: 39-50. https://doi.org/10.1016/j.asoc.2015.04.056
[147]Sachan, R., Choi, T.J. & Ahn, C.W. (2016). A Genetic Algorithm with Location Intelli-gence Method for Energy Optimization in 5G Wireless Networks. Disc. Dyna. Nature Soc., 2016: Art. no. 5348203.
[149]El Moiz Dahi, Z.A., Mezioud, C. & Draa, A. (2017). A 0-1 bat algorithm for cellular net-work optimisation: A systematic study on mapping techniques. Int. J. Reasoning-based In-tel. Syst., 9(1): 22-42. https://doi.org/10.1504/ijris.2017.10007147
[150]Baumgartner, P., Bauernfeind, T., Biro, O., Magele, C., Renhart, W. & Torchio, R. (2018). Synthesis of NFC antenna structure under multi-card condition. International Applied Computational Electromagnetics Society Symposium in Denver, ACES-Denver.
https://doi.org/10.23919/ropaces.2018.8364095
[151]Baumgartner, P., Bauernfeind, T., Biro, O., Magele, C., Renhart, W. & Torchio, R. (2018). Synthesis of NFC antenna structure under multi-card condition. Appl. Comput. Electro. Society J., 33(10): 1161-1163. https://doi.org/10.23919/ropaces.2018.8364095
[152]Sohail, M.F., Ghauri, S.A. & Alam, S. (2017). Channel Estimation in Massive MIMO Sys-tems Using Heuristic Approach. Wireless Pers. Commun., 97(4): 6483-6498.
https://doi.org/10.1007/s11277-017-4849-0
[153]Zheng, S., Gao, S., Yin, Y., Luo, Q., Yang, X., Hu, W., Ren, X. & Qin, F. (2018). A Broadband Dual Circularly Polarized Conical Four-Arm Sinuous Antenna. IEEE Trans. Antennas Prop., 66(1): Art. no. 8103784, 71-80. https://doi.org/10.1109/tap.2017.2772301
[154]Harikrishnan, R., Jawahar Senthil Kumar, V. & Sridevi Ponmalar, P. (2016). A Compara-tive Analysis of Intelligent Algorithms for Localization in Wireless Sensor Networks. Wireless Pers. Commun., 87(3): 1057-1069. https://doi.org/10.1007/s11277-015-2635-4
[155]Liu, D., Zhang, L., Bing, X., Shao, Y. & Xu, B. (2017). Localization Method Based on Modified Cuckoo Difference Optimization for Wireless Sensor Networks. J. Syst. Simul., 29(4): 791-797.
[156]Sivakumar, S. & Venkatesan, R. (2016). Performance evaluation of hybrid evolutionary algorithms in minimizing localization error for wireless sensor networks. J. Scient. Indust. Res., 75(5): 289-295.
[157]Zhou, C., Chen, L., Chen, Z., Li, X. & Dai, G. (2017). A sine cosine mutation based differ-ential evolution algorithm for solving node location problem. Int. J. Wireless Mobile Com-put., 13(3): 253-259. https://doi.org/10.1504/ijwmc.2017.10009499
[158]Sachan, R., Muhammad, Z., Jeong, J., Ahn, C.W. & Youn, H.Y. (2017). MABC: Power-Based Location Planning with a Modified ABC Algorithm for 5G Networks. Disc. Dyn. Nature Soc., 2017: Art. no. 4353612. https://doi.org/10.1155/2017/4353612
[159]SrideviPonmalar, P., Jawahar Senthil Kumar, V. & Harikrishnan, R. (2017). Hybrid firefly variants algorithm for localization optimization in WSN. Int. J. Comput. Intel. Syst., 10(1): 1263-1271. https://doi.org/10.2991/ijcis.10.1.85
[160]Cui, L., Xu, C., Li, G., Ming, Z., Feng, Y. & Lu, N. (2018). A high accurate localization algorithm with DV-Hop and differential evolution for wireless sensor network. Appl. Soft Comput. J., 68: 39-52. https://doi.org/10.1016/j.asoc.2018.03.036
[161]Qin, M. & Zhu, R. (2018). A Monte Carlo localization method based on differential evolu-tion optimizaevolu-tion applied into economic forecasting in mobile wireless sensor networks. Eurasip J. Wireless Commun. Network., 2018(1): Art. no. 32. https://doi.org/10.1186/s1 3638-018-1037-1
[162]Srideviponmalar, P., Jawahar Senthil Kumar, V. & Harikrishnan, R. (2018). Hybrid genet-ic algorithm–differential evolution approach for localization in WSN. Adv. Intel. Syst. Comput., 695: 263-271. https://doi.org/10.1007/978-981-10-7566-7_27
[164]Yu, G. (2017). A dual population based firefly algorithm and its application on wireless sensor network coverage optimization. Int. J. Wirel. Mobile Comput., 13(3): 188-192.
https://doi.org/10.1504/ijwmc.2017.10009494
[165]Qiao, D. & Pang, G.K.H. (2016). A Modified Differential Evolution with Heuristic Algo-rithm for Nonconvex Optimization on Sensor Network Localization. IEEE Trans. Vehic. Technol., 65(3): Art. no. 7055895, 1676-1689. https://doi.org/10.1109/tvt.2015.2409319
[166]Cevik, T. & Gunagwera, A. (2018). Coverage and energy efficiency optimization for ran-domly deployed multi-tier wireless multimedia Sensor Networks. Int. J. Comm. Netw. In-fo. Security, 10(1): 28-36.
[167]Wang, Y.J. & Li, X.J. (2016). Targets coverage algorithm based on three-dimensional di-rectional sensing model. J. Info. Hiding Multimed. Signal Process., 7(1): 145-152. [168]Zhang, Q., & Fok, M.P. (2017). A two-phase coverage-enhancing algorithm for hybrid
wireless sensor networks. Sensors, 17(1): Art. no. 117. https://doi.org/10.3390/s17010117
[169]Qin, N.N. & Chen, J.L. (2018). An area coverage algorithm for wireless sensor networks based on differential evolution. Int. J. Dist. Sensor Networks, 14(8): 1-11.
https://doi.org/10.1177/1550147718796734
[170]Xu, Y., Ye, Y., Zhang, H., Zhang, W. & Lv, Y. (2019). A fast two-objective differential evolution for the two-objective coverage problem of WSNs. Memetic Computing, 11(1): 89-107. https://doi.org/10.1007/s12293-018-0264-7
[171]Céspedes-Mota, A., Castañón, G., Martínez-Herrera, A.F., Cárdenas-Barrón, L.E. & Sar-miento, A.M. (2018). Differential evolution algorithm applied to wireless sensor distribu-tion on different geometric shapes with area and energy optimizadistribu-tion. J. Net. Comp. Appl., 119: 14-23. https://doi.org/10.1016/j.jnca.2018.06.006
[172]Yang, J., Xu, Y., Wei, C. & Jiang, S. (2016). A gateway deployment algorithm in cyber-physical system based on differential evolution. J. Electro. Info. Tech., 38(1): 195-201. [173]Cao, B., Kang, X., Zhao, J., Yang, P., Lv, Z. & Liu, X. (2018). Differential
Evolution-Based 3-D Directional Wireless Sensor Network Deployment Optimization. IEEE Internet of Things J., 5(5): Art. no. 8279426, 3594-3605. https://doi.org/10.1109/jiot.2018.2801623
[174]Wu, D. & Du, F. (2018). A Parallel Ranging-Based Relative Position and Orientation Measurement Method for Large-Volume Components. J. Sensors, 2018: Art. no. 2404825.
https://doi.org/10.1155/2018/2404825
[175]Ren, G., Wu, J. & Versonnen, F. (2018). Bee-based reliable data collection for mobile wireless sensor network. Cluster Computing, 10.1007/s10586-018-2116-0. https://doi.org/ 10.1007/s10586-018-2116-0
[176]Rajalakshmi, S. & Maguteeswaran, R. (2015). Quality of Service Routing in Manet Using a Hybrid Intelligent Algorithm Inspired by Cuckoo Search. Scient. World J., 2015: Art. no. 703480. https://doi.org/10.1155/2015/703480
[177]Wan, Q., Weng, M.J. & Liu, S. (2019). Optimization of wireless sensor networks based on differential evolution algorithm. Int. J. Online Engine., 15(1): 183-195. https://doi.org/10 .3991/ijoe.v15i01.9786
[178]Subramanian, M. & Jaisankar, N. (2018). An optimal path selection in a clustered wireless sensor network environment with swarm intelligence-based data aggregation for air pollu-tion monitoring system. Int. J. Comp. Aided Engine. Tech., 10(4): 378-403.
https://doi.org/10.1504/ijcaet.2018.10012349
[180]Ranjith Kumar, A. & Sivagami, A. (2018). Security Aware Multipath Routing Protocol for WMSNs for Minimizing Effect of Compromising Attacks. J. Netw. Syst. Magt. https://doi. org/10.1007/s10922-018-9477-9
[181]Basha, A.R. & Yaashuwanth, C. (2018). Double secure optimal partial aggregation using trust inference and hybrid syncryption algorithm for wireless sensor networks. J. Comput. Theo. Nanosci., 15(2): 423-436. https://doi.org/10.1166/jctn.2018.7106
[182]Guo, W., Chen, Y., Cai, Y., Wang, T. &Tian, H. (2017). Intrusion detection in WSN with an improved NSA based on the DE-CMOP. KSII Transac. Internet and Info. Syst., 11(11): 5574-5591. https://doi.org/10.3837/tiis.2017.11.022
[183]Xu, Z., Gu, R., Huang, T., Xiang, H., Zhang, X., Qi, L. & Xu, X. (2018). An IoT-oriented offloading method with privacy preservation for cloudlet-enabled wireless metropolitan ar-ea networks. Sensors, 18(9): Art. no. 3030. https://doi.org/10.3390/s18093030
[184]Chen, W., Zhao, H., Li, T. & Liu, Y. (2018). Optimal probabilistic encryption for distrib-uted detection in wireless sensor networks based on immune differential evolution algo-rithm. Wireless Networks, 24(7): 2497-2507. https://doi.org/10.1007/s11276-017-1484-3
[185]Liu, H. (2019). SINR-based multi-channel power schedule under DoS attacks: A Stackel-berg game approach with incomplete information. Automatica, 100: 274-280.
https://doi.org/10.1016/j.automatica.2018.11.034
[186]Wisittipanich, W. & Buakum, D. (2019). Optimal design of pipe diameter in water distri-bution system by multi-objective differential evolution algorithm: A case study of small town in Chiang Mai. Lect. Notes Elect. Engine., 513: 351-360. https://doi.org/10. 1007/978-981-13-1059-1_33
[187]Fu, H., Feng, S., Liu, J. & Tang B. (2016). The modeling and simulation of gas concentra-tion predicconcentra-tion based on De-Eda-Svm. Chinese J. Sensors Actua., 29(2): 285-289.
[188]Prauzek, M., Krömer, P., Rodway, J. & Musilek, P. (2016). Differential evolution of fuzzy controller for environmentally-powered wireless sensors. Appl. Soft Comput. J., 48: 193-206. https://doi.org/10.1016/j.asoc.2016.06.040
[189]Mahmoudzadeh, S., Powers, D.M.W. & Atyabi, A. (2018). UUV's Hierarchical DE-Based Motion Planning in a Semi Dynamic Underwater Wireless Sensor Network. IEEE Trans. Cyber., DOI: 10.1109/TCYB.2018.2837134. https://doi.org/10.1109/tcyb.2018.2837134
[190]Céspedes-Mota, A., Castañón, G., Martínez-Herrera, A.F. & Cárdenas-Barrón, L.E. (2018). Multiobjective Optimization for a Wireless Ad Hoc Sensor Distribution on Shaped-Bounded Areas. Math. Probl. Engine., 2018: Article no. 7873984.
https://doi.org/10.1155/2018/7873984
[191]Hao, X., Wang, L., Liu, J., Xie, L. & Zhang, W. (2018). Resource allocation optimization algorithm based on double populations differential evolution in WSN. J. Communications, 39(4): 68-75.
7
Authors
Muminu O. Adamu
received the B.Sc (Hons) degree in Mathematics/Statistics,
M.Sc degree in Statistics and Ph.D degree in Statistics from the University of
